Two-dimensional photonic crystal optical multiplexer/demultiplexer

ABSTRACT

The present invention provides an optical multiplexer/demultiplexer that can be smaller in size and higher in Q-factor or efficiency. This object is achieved by the following construction. In a slab-shaped body  11 , low refractive index areas  12  having a refractive index lower than that of the material of the body  11  are periodically arranged to construct a two-dimensional photonic crystal, in which a waveguide  13  is formed by not boring holes  12  linearly. A donor type cluster defect  14  is formed by not boring holes  12  at two ore more lattice points located adjacent to the waveguide  13 . With this construction, only a specific wavelength of light included in the light propagating through the waveguide  13  resonates at the donor type cluster  14 , and the light thus trapped is released to the outside (demultiplexing). Conversely, only a specific wavelength of light may be introduced through the donor type cluster defect  14  into the waveguide  13  (multiplexing).

TECHNICAL FIELD

The present invention relates to an optical multiplexing/demultiplexingdevice used for wavelength division multiplexing communication.

BACKGROUND ART

Recently, photonic crystals have been drawing attentions as a newoptical device. A photonic crystal is an optical functional materialhaving a periodic distribution of refractive index, which provides aband structure with respect to the energy of photons. One of itsparticular features is that it has an energy region (called the photonicbandgap) that does not allow the propagation of light.

An example of the application fields of the photonic crystal is theoptical communication. Recent optical communications use the wavelengthdivision multiplexing (WDM) in place of a conventional method called thetime division multiplexing (TDM). The wavelength division multiplexingis a communication method in which plural wavelengths of light, eachcarrying a different signal, propagate through a single transmissionline. This method has drastically increased the amount of informationthat can be transmitted per unit of time.

In wavelength division multiplexing, plural wavelengths of light aremixed at the inlet of the transmission line, and the mixture of light isseparated into the plural wavelengths of light at the outlet. Thisrequires an optical multiplexer and an optical demultiplexer, orwavelength filters. A type of demultiplexers currently used is arrayedweveguide grating (AWG). AWG uses a normal type of waveguide. With thisconstruction, it is currently necessary to make the device as large asroughly several square centimeters to adequately decrease the loss oflight.

Taking into account the above-described situation, research has beenconducted on the miniaturization of demultiplexers by using a devicecomposed of a photonic crystal as the multiplexer or demultiplexer, asdisclosed in the Japanese Unexamined Patent Publication No. 2001-272555,which is referred to as “Prior Art Document 1” hereinafter. A briefdescription of the demultiplexer using a photonic crystal follows. Whenan appropriate defect is introduced in the photonic crystal, the defectcreates an energy level, called the defect level, within the photonicbandgap. This state allows the light to exist only at a specificwavelength corresponding to the energy of the defect level within thewavelength range corresponding to the energies included in the photonicbandgap. There, when the defects in the crystal have a lineararrangement, the device functions as an optical waveguide, while itfunctions as an optical resonator when the defect or defects have apoint-like form in the crystal.

When a ray of light including various wavelength components ispropagated through the waveguide of a photonic crystal having anappropriate point defect located in proximity to the waveguide, only aspecific component of light having a wavelength corresponding to theresonance frequency of the point defect is trapped by the point defect.Taking out the light will make the device a demultiplexer for a desiredwavelength. In reverse, a ray of light having a wavelength correspondingto the resonance frequency may be introduced from the point defect intothe photonic crystal and propagated through the waveguide with othercomponents of light having different wavelengths. This makes the devicea multiplexer for a desired wavelength.

For photonic crystals used as a multiplexer or demultiplexer, bothtwo-dimensional and three-dimensional crystals may be used, each ofwhich has its own features and advantages. The following descriptiontakes the two-dimensional crystal as an example, which is relativelyeasier to manufacture. In two-dimensional crystals, there is asignificant difference in the refractive index in the directionperpendicular to its surface, or in the orthogonal direction, betweenthe crystal body and the air so that it can confine light in theorthogonal direction.

Prior Art Document 1 discloses a study in which cylindrical holes of thesame diameter are periodically arranged in a slab made of InGaAsP, aline of the cylindrical holes is filled to form an optical waveguide,and a defect is introduced by designing at least one of the cylindricalholes to have a diameter different from that of the other holes tocreate an optical resonator

In this structure, the lattice constant a is set at a valuecorresponding to the wavelength of light that should be propagated (inthe above example, it is set at 1.55 μm, which is one of the wavelengthsgenerally used in wavelength division multiplexing communications), theradius of the cylindrical hole formed at each lattice point is set at0.29a except for one hole whose radius is set at 0.56a to create a pointdefect. With this configuration, a ray of light having a normalizedfrequency f=0.273 is radiated upwards and downwards from the pointdefect in the orthogonal direction of the slab. The Q-factor obtainedthereby is about 500. It should be noted that a normalized frequency isa non-dimensional value obtained by multiplying the frequency of lightby a/c, where c is the speed of light. The Q-factor indicates thequality of the resonator. The higher the Q-factor is, the higher thewavelength resolution. When the radius of one cylindrical hole is 0.56aand that of another hole is 0.58a, the normalized frequencies will be0.2729 and 0.2769, respectively, so that two rays of light havingdifferent wavelengths are generated. The Q-factors for both holes areabout 500.

As mentioned above, Prior Art Document 1 teaches that two-dimensionalphotonic crystals can be used as optical demultiplexers. Thesedemultiplexers, however, need further improvements with regard to somepoints relating to Q-factor, as explained below. In the case of PriorArt Document 1, the Q-factor is about 500. With this value, thewavelength resolution of the above-described optical resonator is about3 nm for the wavelength band of 1.55 μm, because the wavelengthresolution of an optical resonator for wavelength λ is given by λ/Q. Fora resonator to be applicable to high-density wavelength divisionmultiplexing optical communications, however, the wavelength resolutionmust be about 0.8 nm or less, meaning that the Q-factor must be about2000 or greater. One possible factor against the improvement in Q-factorin Prior Art Document 1 is an increase in the loss of energy of light inthe orthogonal direction due to the introduction of the point defect.

The decrease in Q-factor may also result from asymmetry that may beintroduced into a point defect. For example, as mentioned in Prior ArtDocument 1, a point defect may be designed to be asymmetrical in thedirection orthogonal to the plane so that light is taken out only fromone side of the two-dimensional plane. Otherwise, a point defect may bedesigned to be asymmetrical in the in-plane direction to take out a rayof polarized light. For example, when the point defect is circular, thelight emitted from the defect is not polarized. However, it is oftennecessary to linearly polarize the light so as to couple it to anexternal optical system, or for some other purposes.

The present invention has been accomplished to solve such problems, andone of its objects is to provide an optical multiplexer/demultiplexerthat can be smaller in size and higher in Q-factor or efficiency.Another object is to provide an optical multiplexer/demultiplexer thatshows a high level of efficiency even when it has asymmetry introducedin the orthogonal direction or when polarized light needs to beobtained.

DISCLOSURE OF THE INVENTION

To solve the aforementioned problems, in the first mode of the presentinvention, the two-dimensional photonic crystal opticalmultiplexer/demultiplexer includes:

a) a slab-shaped body;

b) a plurality of modified refractive index areas having a refractiveindex different from that of the body, which are periodically arrangedin the body;

c) a waveguide formed in the body by creating a linear defect of themodified refractive index areas; and

d) a cluster defect located in proximity to the waveguide and composedof two or more defects adjacent to each other.

Also, in the second mode of the present invention, the two-dimensionalphotonic crystal optical multiplexer/demultiplexer includes:

a) a slab-shaped body;

b) two or more forbidden band zones formed in the body;

c) a plurality of modified refractive index areas having a refractiveindex different from that of the body, which are periodically arrangedwithin each of the forbidden band zones of the body in a periodicpattern that is differently determined for each of the forbidden bandzones;

d) a waveguide passing through all the forbidden band zones, which isformed by creating a linear defect of the modified refractive indexareas within each of the forbidden band zones; and

e) point-like defects each formed in proximity to the waveguide withineach of the forbidden band zones.

The first mode of the present invention is described. According to thepresent invention, a plate-shaped slab with its thickness adequatelysmaller than its size in the in-plane direction is used as the body ofthe two-dimensional photonic crystal optical multiplexer/demultiplexer.On this body, modified refractive index areas having a refractive indexdifferent from that of the body are periodically arranged. The presenceof the periodical arrangement of the modified refractive index areasgenerates a photonic bandgap, which does not allow the presence of lightwhose energy falls within the range of the photonic bandgap. This meansthat the light having a wavelength corresponding to that energy cannotpass through the body.

The refractive index of the modified refractive index area may be higheror lower than that of the body. From the viewpoint of easier materialselection, however, it is recommendable to make the modified refractiveindex area from a material having a low refractive index, because thebody is usually made from a material having a high refractive index.

The low refractive index area may be created by embedding a materialhaving a low refractive index in the body or just forming a hole in thebody. In the latter case, the air constitutes the modified refractiveindex area. Practically, air is the material that has the lowestrefractive index. Therefore, forming a hole is advantageous to increasethe difference in the refractive index between the modified refractiveindex area and the body. Furthermore, forming a hole is easier thanembedding a different material.

In the following description, the points at which the modifiedrefractive index areas are periodically placed are called the latticepoints. The lattice points can be arranged in various patterns. Typicalexamples include the square lattice pattern or triangular latticepattern.

In a photonic crystal having a periodicity as described above, a defectof a modified refractive index area at a lattice point creates adisorder in the periodicity. If a parameter or parameters relating tothe defect are appropriately determined, the disorder in the periodicitycreates a “defect level” within the photonic bandgap, which generates apoint that allows the presence of light within the body in which lightis not basically allowed to exist. This is called a point defect.Creating point defects along a line forms a waveguide within the body,which light can pass through. This is called the line defect. A linedefect may take the form of a bent or curved line as well as a straightline. A line defect may be composed of a single row of lattice points ora bundle of multiple rows of lattice points lying side by side.

In the case of forming the modified refractive index areas with theholes, the easiest method of creating a defect at a lattice point is tofill the hole at the lattice point with the material of the body, thatis, to omit boring a hole at the lattice point. Alternatively,increasing the diameter of a hole makes the hole a defect. A defectcreated by not boring a hole at a lattice point is called the donor typedefect, and a defect created by increasing the diameter of the hole iscalled the acceptor type defect.

In the first mode of the present invention, the donor type defect andthe acceptor type defect are described. This specification refers to therefractive index because the present invention concerns light includinginfrared and ultraviolet rays. In general, however, a photonic crystalis created by a periodic difference in the dielectric constant.Therefore, to create a defect, the dielectric constant of one of themodified refractive index areas (or lattice points) periodicallyarranged in the body should be changed. A lattice point whose dielectricconstant is higher than that of the others is called the donor typedefect, and that with lower dielectric constant is called the acceptortype defect. When, as described previously, holes are arranged in a bodymade from a certain material and no hole is bored (or the hole is filledwith the body material) at a certain lattice point to create a defect,the dielectric constant at the point is higher than that of air, so thatthe point becomes a donor type defect. In contrast, increasing thediameter of the hole at a lattice point will decrease the dielectricconstant at that point, and the point will be an acceptor type defect.

Another type of defect whose characteristics are different from thedefect made of a single lattice point is formed by making defects at twoor more lattice points adjacent to each other in proximity to thewaveguide. Hereinafter, a defect composed of a single lattice point iscalled the “point defect.” The defect disclosed in Prior Art Document 1is the point defect in this sense. On the other hand, the defect used inthe first mode of the present invention is composed of two or morelattice points adjacent to each other, which is called the “clusterdefect” hereinafter. Further, the “point defect” and “cluster defect”are generally called the “point-like defect” in this specification.These will be used in the second mode of the present invention describedlater.

In the above-described construction, a desired defect level can becreated within the photonic bandgap by appropriately determining theparameters of the cluster defect, such as the number or arrangement oflattice points included in a cluster defect, the position of the clusterdefect (e.g. distance from the waveguide), or the lattice constant a ofthe body. Then, among various wavelengths of light passing through thewaveguide, only the light having the wavelength corresponding to thedefect level resonates at the position of the defect. The resonant lightis emitted in the orthogonal direction of the photonic crystal. Adesired wavelength of light can be obtained by adjusting theaforementioned parameters so that the defect level is created at anappropriate energy level.

When the cluster defect is composed of two or more defects lying on astraight line, the defects generate a ray of light polarized in thewidth direction of the cluster defect.

By designing the cluster defect to be asymmetrical in the orthogonaldirection, it is possible to produce an asymmetrical emission of lightin the upward and downward directions from the two-dimensional photoniccrystal. One method of creating an asymmetrical defect is to create amodified refractive index area whose thickness extends from one face ofthe body to an intermediate point inside the body. The thickness shouldbe preferably from 5 to 40%, more preferably from 20 to 30%, of thethickness of the body, as described later.

To make a cluster defect asymmetrical in the orthogonal direction, it isnot necessary to make each lattice point asymmetrical, as describedabove. For example, in a cluster defect composed of two lattice pointsadjacent to each other, the above-described work (i.e. forming an areahaving low refractive index on one side only) may be performed on anintermediate point between the two lattice points.

So far, this specification has described the function of photoniccrystals as a demultiplexer. It should be noted that the above-describedphotonic crystals may be used as a multiplexer. When a ray of lighthaving a wavelength corresponding to the energy of the defect level isintroduced into the cluster defect, it will be mixed with the lightpassing through the waveguide.

It is also possible to mix or separate two or more wavelengths of lightby providing two or more cluster defects having different numbers orarrangements of lattice points.

The second mode of the present invention is described. The descriptionof the first mode has shown that optical multiplexing/demultiplexing canbe performed at various wavelengths by changing the number orarrangement of lattice points at which the defects are located. It hasbeen also explained that a preferable form of the modified refractiveindex area is a hole, and the defect should be preferably a donor typedefect obtained by not boring the hole. The donor type defect, however,has less degree of freedom for wavelength variation than the acceptortype defect created by increasing the diameter of the hole. This isbecause the acceptor type defect allows an arbitrary variation of thehole size, whereas the donor type defect is created by simply fillingthe hole with the body material, and this method has little degree offreedom for variation. Grouping donor type defects into a cluster typedefect according to the first mode of the present invention provides anadditional degree of freedom for changing the number or arrangement oflattice points included in the cluster defect. This degree of freedom,however, is still limited. The second mode of the present inventionsolves this problem concerning the donor type defect, as describedbelow.

According to the second mode of the present invention, the body isdivided into the same number of zones as the multiplexing/demultiplexingwavelengths, and the modified refractive index areas are periodicallyarranged in a different cycle within each zone. The zone is called theforbidden band zone in this specification.

Similar to the first mode, the modified refractive index area should bepreferably made from a material having a low refractive index, andpreferably made from air, i.e. a hole.

As in the first mode, a waveguide that passes through all the forbiddenband zones is formed so as to let light pass through each forbidden bandzone and be mixed. Furthermore, a point-like defect formultiplexing/demultiplexing is formed in each forbidden band zone. Asexplained previously, the “point-like defect” may be either a pointdefect composed of a single lattice point or a cluster defect composedof plural lattice points adjacent to each other. The point-like defectsformed in the forbidden band zones are designed so that they differ fromeach other in resonance wavelength. This means that a two-dimensionalphotonic crystal optical multiplexer/demultiplexer having n pieces offorbidden band zones is capable of multiplexing/demultiplexing n piecesof wavelengths of light. This structure of two-dimensional photoniccrystal in which plural forbidden band zones are present is called the“in-plane heterostructure”.

The arrangement cycle (or the lattice constant) and point-like defectsof the modified refractive index areas in each forbidden band zone aredetermined corresponding to the wavelengths of light to bemultiplexed/demultiplexed. The ratio of the size of the modifiedrefractive index area in one forbidden band zone to that in anothershould be preferably equal to the ratio of the arrangement cycle of themodified refractive index areas in the former forbidden band zone tothat in the latter. When all the cluster defects placed in the forbiddenband zones have the same form, the wavelength for themultiplexing/demultiplexing of light at each cluster defect isdetermined by the arrangement cycle of each forbidden band zone. It isnaturally allowable to form a cluster defect having a different latticepoint number or a different form in each forbidden band zone. Thevarious types of cluster defects mentioned in the first mode can be alsoused hereby.

The principal object of the second mode of the present invention is toincrease the degree of freedom for the donor type defects, which arecreated by not boring holes in the body. This construction of the secondmode is also applicable to the acceptor type defect and provides aspecific advantage for it. When two or more wavelengths of light are tobe mixed or separated by acceptor type defects created by increasing thediameter of the hole at a certain lattice point, it has beenconventionally necessary to form plural holes having different diametersin a single body slab. This construction, however, decreases theQ-factor. The second mode of the present invention can be preferablyused to avoid such a decrease in Q-factor. That is, in plural forbiddenband zones, modified refractive index areas are formed with differentarrangement cycles corresponding to the plural wavelengths for opticalmultiplexing/demultiplexing. The ratio of the size of the modifiedrefractive index area in one forbidden band zone to that in another, andthe ratio of the size of the acceptor type point defect placed in oneforbidden band zone to that in another, are set equal to thepredetermined ratio of the arrangement cycle of the modified refractiveindex areas in the former forbidden band zone to that in the latter.This construction enables the multiplexing/demultiplexing of pluralwavelengths of light without decreasing the Q-factor.

In the first mode of the present invention, the introduction of acluster defect enables a multiplexer/demultiplexer to have higherQ-factor than in the case of using a point defect composed of a singlelattice point. This is because the presence of the cluster defectincreases the effective refractive index around the defect, whichimproves the light confining efficiency. The opticalmultiplexer/demultiplexer also exhibits high efficiency when it hasasymmetry in the orthogonal direction or when it is used to producepolarized light.

In the second mode of the present invention, the in-planeheterostructure provides a higher degree of freedom for the selection ofwavelengths for the multiplexing/demultiplexing of light even in thecase of using donor type defects. The Q-factor obtained thereby isapproximately equal to that of a photonic crystal for themultiplexing/demultiplexing of a single wavelength of light. When thedonor type defect having a high Q-factor according to the first mode isused to construct the structure of the second mode, it will berelatively easy to obtain a device for multiplexing/demultiplexingvarious wavelengths of light with a high Q-factor. The second mode canalso be effectively applied to the acceptor type defect.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration showing a two-dimensional photoniccrystal having a donor type cluster defect as the first mode of thepresent invention.

FIG. 2 is a schematic illustration showing examples of donor typecluster defects.

FIG. 3 shows graphs indicating the frequency band of the light passingthrough the waveguide.

FIG. 4 is a graph showing the defect level created by the donor typecluster defect with a single lattice point filled.

FIG. 5 is a graph showing the defect level created by the donor typecluster defect with two lattice points filled.

FIG. 6 is a graph showing the defect level created by the donor typecluster defect with three lattice points filled as a triangle.

FIG. 7 is a graph showing the defect level created by the donor typecluster defect with three lattice points filled along a straight line.

FIG. 8 is a graph showing the map of electromagnetic field around thedonor type cluster defect with two lattice points filled.

FIG. 9 is a graph showing the map of electromagnetic field around thedonor type cluster defect with three lattice points filled.

FIG. 10 is a graph showing the relation between the location of defectand Q_(p) or Q_(s).

FIG. 11 is a table showing the relation between the location of defectand Q-factor.

FIG. 12 is a graph showing the relation between the location of defectand Q_(p)/Q_(s).

FIG. 13 is a graph showing the polarization characteristic of the donortype cluster defect with three lattice points filled along a straightline.

FIG. 14 is a schematic illustration showing an example of the donor typecluster defect asymmetrical in the orthogonal direction.

FIG. 15 is a graph showing the relation between the depth h of the holebored at a point-like defect and the upward and downward emission ratio.

FIG. 16 is a graph showing the relation between the depth h of the holebored at a point-like defect and the Q-factor of the resonator.

FIG. 17 is a schematic illustration showing an example of the in-planeheterostructure having donor type cluster defects.

FIG. 18 is a schematic illustration showing an example of the in-planeheterostructure having acceptor type cluster defects.

FIG. 19 shows tables showing the relation between the in-planeheterostructure and the Q-factor.

BEST MODE FOR CARRYING OUT THE INVENTION (1) Embodiment of the FirstMode

(1-1) Construction

As an embodiment of the first mode of the present invention, atwo-dimensional photonic crystal as schematically illustrated in FIG. 1is described. The plate shown in FIG. 1 is a slab (or body) 11. Forinfrared light having a wavelength λ=1.55 μm used in normal opticalcommunications, the slab 11 may be made from InGaAsP, which istransparent to that wavelength of infrared light. The slab 11 has holes12 periodically arranged as the modified refractive index areas (or lowrefractive index areas) as shown by the white circles. The holes 12shown in FIG. 1 are arranged in a triangular lattice pattern, which maybe arranged in various patterns, such as a square lattice pattern.

Waveguide 13 is formed by not boring holes along a linear zone indicatedby the solid arrow in FIG. 1. A donor type cluster defect 14 is formedby not boring holes at plural lattice points within the area indicatedby the white arrow. In the following description, the process of forminga donor type cluster defect is often described as “fill the latticepoints” because, on the drawing, the defect is illustrated as latticepoints composed of holes filled with the body material.

The example of FIG. 1 shows a donor type cluster defect with threelattice points filled. FIG. 2 shows various constructions for the donortype cluster defect. The examples shown in FIG. 2 have two or threelattice points filled. Though not shown in the drawing, it should benoted that it is possible to create a donor type cluster defect withmore than three lattice points filled. Regarding the construction withthree lattice points filled, FIG. 2 shows three types of defects. Amongthese types, the defect composed of three lattice points arranged as atriangle is called the “triangular defect”, and the defect composed ofthree lattice points lying on a straight line is called the “straightline defect.” Also, for the purpose of comparison, an example of thedonor type defect (or donor type point defect) composed of a singlelattice point is shown in FIG. 2.

(1-2) Check of Multiplexing/Demultiplexing Functionality

This section examines whether the above-described construction isactually applicable to the multiplexing/demultiplexing of light. Thefirst step is to determine the wavelength band within the photonicbandgap in which the waveguide allows light to pass through, and thesecond step is to examine whether the donor type defect creates a defectlevel within the wavelength band. The analysis method used hereby iscalled the “two-dimensional plane wave expansion method”.

In the plane wave expansion method, light propagating through a spacehaving a periodic distribution of dielectric constant is expressed by acomposition of plane waves. In the case of the TE mode in which theelectric field oscillates in the in-plane direction and the magneticfield oscillates in the orthogonal direction, the Maxwell's equationsfor the magnetic field is written as follows:

$\begin{matrix}{{{{\frac{\partial\;}{\partial x}\left\lbrack {\frac{1}{ɛ_{r}(r)}\frac{\partial H_{z}}{\partial x}} \right\rbrack} + {\frac{\partial\;}{\partial y}\left\lbrack {\frac{1}{ɛ_{r}(r)}\frac{\partial H_{z}}{\partial y}} \right\rbrack} + {\frac{\omega^{2}}{c^{2}}H_{z}}} = 0},} & (1)\end{matrix}$where ω is the angular frequency of light, H_(z)=H_(z)(x, y, ω) is themagnetic field in z-direction at a point on the plane (H_(x) and H_(y)are zero), and c is the speed of light. e_(r)(r) represents the periodicdistribution of dielectric constant. Expansion of e_(r)(r) by Fourierseries and expansion of H_(z)(x, y, ω) by Bloch theorem give thefollowing equations:

$\begin{matrix}\begin{matrix}{\frac{1}{ɛ_{r}(r)} = {\sum\limits_{G}^{\;}\;{{\kappa(G)}\exp\left\{ {{jG} \cdot r} \right\}}}} \\{{{H_{z}\left( {x,\omega} \right)} = {\sum\limits_{G}^{\;}\;{{h\left( {k,G} \right)}\exp\left\{ {{j\left( {k + G} \right)} \cdot r} \right\}}}},}\end{matrix} & (2)\end{matrix}$where k is the wave number vector and G is the reciprocal latticevector. κ(G) and h(k,G) are expansion coefficients. Substitutingequation (2) into equation (1) gives the following equation for h(k, G),with G specified arbitrarily

$\begin{matrix}{{\sum\limits_{G^{\prime}}^{\;}\;{{\left( {k + G} \right) \cdot \left( {k + G^{\prime}} \right)}{\kappa\left( {G - G^{\prime}} \right)}{h\left( {k,G^{\prime}} \right)}}} = {\left( \frac{\omega}{c} \right)^{2}{h\left( {k,G} \right)}}} & (3)\end{matrix}$Given a specific value of wave number vector k, this equation determines(ω/c)² as the characteristic value, from which the correspondingfrequency, or corresponding energy, is determined. Calculation offrequencies co for various wave number vectors k enables the calculationof the photonic band structure.

Using equation (3), the frequency range of light propagating through thewaveguide of a two-dimensional photonic crystal having no point-likedefect has been calculated for the TE mode. The result is shown in FIG.3. The right side graph is an enlarged view of a part of the left sidegraph. FIG. 3 shows that light can propagate in two guided modes: zerothorder mode, indicated by the black dots, and first order mode, indicatedby the white dots. It is likely that the zeroth order mode provideshigher efficiency because it is the single mode and convenient forexternal systems. The light located on the high-frequency side of thesolid line named “Light Line” tends to be combined with the lightexisting in the free space and having the same frequency and the samein-plane wave number, whereby it leaks in the upward and downwarddirections, and the propagating efficiency is deteriorated. Therefore,it seems that the light having a normalized frequency within the rangefrom 0.267 to 0.280, which is indicated by the black dots and narrowsolid lines in the right side graph of FIG. 3, is propagated mostefficiently through the waveguide. In other words, what is necessaryhereby is to determine the lattice constant a so that the desiredwavelength of light falls within the range from 0.267 to 0.280 innormalized frequency. For example, if the body is made from InGaAsP andthe wavelength of the light used is 1.55 μm, a calculation based on theabove-specified range of normalized frequency shows that the latticeconstant a should be within the range from 0.42 to 0.43 μm.

The defect level has been calculated for the following types of clusterdefects among those shown in FIG. 2: the type with two lattice pointsfilled, the type with three lattice points filled as a triangle, and thetype with three lattice points filled along a straight line. Also, forthe purpose of comparison, the calculation has been performed on thedonor type point defect composed of a single lattice point filled. Theresult is shown in FIGS. 4 to 7. In the case of the donor type pointdefect as a comparative example, the defect level is not created withinthe frequency range from 0.267c/a to 0.280c/a (which is referred to asthe “available frequency range” hereinafter) within which light canpropagate through the waveguide, as shown in FIG. 4, so that thisconstruction cannot be used as a multiplexer/demultiplexer.

In the case of the cluster defect created by filling two neighboringlattice points, on the other hand, only one defect level is createdwithin the available frequency range, as shown in FIG. 5, so that thisconstruction can be used as a multiplexer/demultiplexer. In the case ofthe cluster defect with three lattice points filled as a triangle,plural defect levels are created within the available frequency range,as shown in FIG. 6. Among these defect levels, the one located close tothe normalized frequency 0.268 is isolated and adequately far from theother defect levels located on the higher frequency side. Therefore,this construction can be used as a multiplexer/demultiplexer. In thecase of the cluster defect with three lattice points filled along astraight line parallel to the waveguide, only one defect level iscreated within the available frequency range, as shown in FIG. 7, sothat this construction can be used as a multiplexer/demultiplexer.

The distribution of the electromagnetic field has been calculated forthe following types which have been proved to be available formultiplexer/demultiplexers: the type with two neighboring lattice pointsfilled, the type with three lattice points filled as a triangle, and thetype with three lattice points filled along a straight line parallel tothe waveguide. The result is shown in FIGS. 8 and 9. In these figures,the arrows indicate the electric field vectors parallel to the plane ofdrawing, and the grayscale patterns represent the amplitude of themagnetic field in the direction perpendicular to the plane of drawing.In the case of the defect with two lattice points filled or threelattice points filled along a straight line, the light that resonates atthe defect is in the mode that propagates the light to the filledlattice points. The electric field is strong in the directionperpendicular to the line connecting the filled lattice points. Thissuggests that the resonant light has a characteristic close to linearlypolarized light. In the case of the defect with three lattice pointsfilled as a triangle, on the other hand, the resonant mode is such thatthe light propagates from the centroid to each apex of the triangle.This suggests that the electromagnetic field is distributed rathersymmetrically, so that the polarization degree is lower than in theaforementioned two cases.

(1-3) Calculation of Q-factor

The Q-factor has been calculated for the three cases described in theprevious paragraph, using the Finite-Difference Time-Domain method (K.S. Yee, “IEEE Trans. Antennas Propagat.” AP-Vol. 14, pp. 302-307). Thefrequency dependency around the defect level has been calculated withrespect to the intensity of the electromagnetic wave radiated, and theQ-factor has been calculated from the peak intensity and the full widthat half maximum.

The Q-factor of a two-dimensional photonic crystal is determined byQ_(p), which represents the coupling between the point-like defect andthe waveguide, and Q_(s), which represents the coupling between thepoint-like defect and the external (the space outside the surface).Q_(p) is determined by the distance between the point-defect and thewaveguide. Therefore, in order to investigate the change in Q-factorwith respect to the type of the point-like defect, Q_(s) has beencalculated on the assumption that the distance between the point-likedefect and the waveguide is infinite. The result is that Q_(s)=1354 whentwo lattice points are filled, Q_(s)=2529 when three lattice points arefilled as a triangle, and Q_(s)=5215 when three lattice points arefilled along a straight line. In the case of the acceptor type pointdefect disclosed in Prior Art Document 1, the same calculation showsthat Q_(s)=924.

The calculation suggests that the Q-factor of the donor type clusterdefect can be higher than that of the acceptor type point defect.Particularly, it is expected that the defect with three lattice pointsfilled along a straight line has the highest Q-factor. Taking this intoaccount, the dependency of Q_(s) and Q_(p) on the distance between thepoint-like defect and the waveguide has been investigated. The result isshown in FIG. 10. In this figure, the abscissa indicates the distancebetween the lattice points filled along a straight line and thewaveguide, represented by the number of columns of holes. Using Q_(s)and Q_(p), a Q-factor can be calculated by equation 1/Q=1/Q_(s)+1/Q_(p).From this equation and FIG. 10, the Q-factor can be obtained as shown inFIG. 11. This figure shows that the Q-factor is from 2012 to 4666, whichis far greater than that in the case of Prior Art Document 1, i.e. about500.

FIG. 11 shows that the Q-factor increases as the distance between thepoint-like defect and the waveguide increases. However, when thedistance is too large, the light reaching the point-like defectdecreases in the case of a demultiplexer, or the light reaching thewaveguide decreases in the case of a multiplexer. Since these situationsare undesirable for multiplexers/demultiplexers, the distance must beappropriately determined, taking into account the trade-off between theQ-factor and the delivery of light between the point-like defect and thewaveguide. It seems that the highest efficiency is obtained whenQ_(p)=Q_(s). In FIG. 12, this condition is best satisfied when thepoint-like defect is located at the fourth column of holes from thewaveguide.

The description in the previous paragraph focused on the efficiency as amultiplexer/demultiplexer. It is also possible to intentionally increaseQ_(p) and decrease Q_(s). This setting allows the device to be used as awavelength detection device for extracting and monitoring a small amountof light having a specific wavelength passing through the waveguide.

(1-4) Polarization Characteristics

As mentioned in section (1-2), in the case of filling two lattice pointsor three lattice points along a straight line, it is expected that thelight emitted thereby is linearly polarized. To confirm this idea, thepolarization characteristics of the light emitted in the case of threelattice points filled along a straight line has been calculated. Theresult is shown in FIG. 13. In this figure, the abscissa indicates thein-plane angle from the line of the filled lattice points, and theordinate indicates the amplitude of light at the angle. The amplitude isapproximately zero in the direction where the angle is zero degree,while it is maximized in the direction where the angle is 90 degrees.This means that the light is strongly polarized in the directionperpendicular to the line of the filled lattice points.

(1-5) Controlling the Upward and Downward Emission Ratio of the DonorType Cluster Defect

The foregoing descriptions assumed that the point-like defect wassymmetrical in the orthogonal direction. That is, it was assumed thateach lattice point was completely filled with the low refractive indexmaterial. With this construction, the point-like defect emits light inboth upward and downward directions.

This section describes a calculation carried out under the conditionthat the donor type cluster defect is asymmetrical in the upward anddownward direction, as shown in FIG. 14. In the example of FIG. 14, thebody having a thickness of 0.6a is provided with three lattice pointsfilled along a straight line and two intermediate holes having a radiusr=0.29a and depth h (<0.6a) bored between the filled lattice points.Under this condition, the relation between the depth normalized by thelattice constant, h/a, and the upward and downward emission ratio hasbeen calculated. The result is shown in FIG. 15. Within the range of h/ashown in this figure (i.e. 0.05-0.4), the upward and downward emissionsfrom the defect are asymmetrical. Particularly, the upward and downwardemission ratio is approximately 2.0 or higher within the range where h/ais between 0.2 and 0.4. FIG. 16 shows the relation between Q-factor andh/a. It shows that the Q-factor is rather low within the range where theupward and downward emission ratio is high. Even within this range,however, the Q-factor obtained hereby is higher than in the case ofPrior Art Document 1.

(2) Embodiment of the Second Mode

FIG. 17 shows an example of the in-plane heterostructure as anembodiment of the second mode of the present invention. This figureshows an in-plane heterostructure consisting of two forbidden bandzones. It consists of a crystal having holes (or low refractive indexmaterials) arrayed at arrangement cycle a₁ and another crystal havingholes arrayed at arrangement cycle a₂ connected along the central lineindicated by the chain line. The first crystal having the arrangementcycle a₁ is called the first forbidden band zone and the second crystalhaving the arrangement cycle a₂ is called the second forbidden band zonehereinafter. The diameter of the holes in the first forbidden band zoneis denoted by b₁, and that in the second forbidden band zone is denotedby b₂. The waveguides located on both sides of the chain line arearranged so that they lie on the same straight line. Donor type clusterdefects having the same form are created in both first and secondforbidden band zones. In this structure, a₁/a₂ is designed to be equalto b₁/b₁. Since the arrangement cycle of the holes determines the sizeof the donor type cluster defect, the ratio of the size of the donortype cluster defect in the first forbidden band zone to that in thesecond forbidden band zone is also equal to a₁/a₂.

In the example of FIG. 17, the donor type cluster defect is composed ofthree lattice points filled as a triangle. It is also possible to use adonor type cluster defect composed of three lattice points filled alonga straight line, or other types. The point-like defect may be anacceptor type point defect, as shown in FIG. 18. In this case, the firstforbidden band zone is provided with one acceptor type point defecthaving a diameter c₁, and the second forbidden band zone is providedwith one acceptor type point defect having a diameter c2. The values ofa₁/a₂, b₁/b₂ and c₁/c₂ should be equal to each other.

The Q-factor has been calculated for a structure having donor typecluster defects that are located as shown in FIG. 17 but each composedof three lattice points filled along a straight line, and for thestructure shown in FIG. 18, under the following conditions: a₁ is equalto a₂; a₁ is 1% larger than a₂; and a₁ is 1% smaller than a₂. Thestructural difference between +1% and −1%, or total 2%, corresponds tothe difference of 30 nm in the resonance wavelength in the 1.55 μm band.The following conditions is further assumed: b₁=0.29a₁, b₂=0.29a₂,c₁=0.54a₁, c₂=0.54a₂. FIG. 19 shows the Q-factors calculated. For FIGS.17 and 18, (1−a₂/a₁) has been defined as the percentage of structuralchange. In the case of using donor type cluster defects, the Q-factor is2885-2891, which is adequately large. In the case of using acceptor typepoint defects, the Q-factors obtained are comparable to that of thetwo-dimensional photonic crystal using an acceptor type defect disclosedin Prior Art Document 1. The structural difference does not cause anysignificant decrease in Q-factor.

(3) Example of Fabricating a Two-Dimensional Photonic Crystal of theFirst and Second Modes of the Present Invention.

A method of fabricating a two-dimensional photonic crystal is disclosedin paragraphs [0037] to [0044] of the Japanese Unexamined PatentPublication No. 2001-272555, in which air is used as the low refractiveindex material. This method is briefly described here (for more detail,the aforementioned publication can be consulted). A slab to be used asthe body is created by forming a layer of the slab material on asubstrate by crystal growth. An example of the slab material is InGaAsPin the case where the wavelength band of the light of interest is the1.55 μm band. A photoresist layer is formed on the surface of the slab,and an electron beam is irradiated onto it to draw a patterncorresponding to the low refractive index materials and the acceptortype point defects. The surface is gas-etched to form the low refractiveindex materials and the acceptor type point defects.

To fabricate a two-dimensional photonic crystal of the first mode of thepresent invention by the above-described method, the pattern-drawingprocess should be controlled so that a donor type cluster defect isintroduced into the pattern by not irradiating the electron beam ontothe area where the donor type cluster defect is to be located.Similarly, an in-plane heterostructure of the second mode of the presentinvention can be introduced by controlling the pattern-drawing processaccording to the structure.

1. A two-dimensional photonic crystal optical multiplexer/demultiplexer,comprising: a slab-shaped body; a plurality of modified refractive indexareas having a refractive index different from that of the body, whichare periodically arranged in the body; a waveguide formed in the bodymaking defects of the modified refractive index areas linearly; and acluster defect located in proximity to the waveguide and composed of twoor more adjacent defects without intervening non-defects, the defectsbeing locations where the modified refractive index areas should exist,based on their periodic arrangement, but do not.
 2. The two-dimensionalphotonic crystal optical multiplexer/demultiplexer according to claim 1,wherein the cluster defect is composed of three defects adjacent to eachother in the form of a triangle.
 3. The two-dimensional photonic crystaloptical multiplexer/demultiplexer according to claim 1, wherein thecluster defect is composed of three defects adjacent to each other on astraight line parallel to the waveguide.
 4. The two-dimensional photoniccrystal optical multiplexer/demultiplexer according to claim 3, whereinthe cluster defect composed of three defects adjacent to each other on astraight line is located on a fourth row of the modified refractiveindex areas from the waveguide.
 5. A two-dimensional photonic crystaloptical multiplexer/demultiplexer, comprising: a slab-shaped body; twoor more forbidden band zones formed in the body; a plurality of modifiedrefractive index areas having a refractive index different from that ofthe body, which are periodically arranged within each forbidden bandzone of the body with a periodic cycle that is differently determinedfor each forbidden band zone; a waveguide passing through all theforbidden band zones, which is formed by making defects of the modifiedrefractive index areas linearly within each forbidden band zone; andpoint-like defect resonators each composed of a point-like defect whichis composed of one or more defects adjacent to each other and is formedin proximity to the waveguide within each of the forbidden band zones.6. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer according to claim 5, wherein at least one ofthe point-like defects each formed in proximity to the waveguide withineach of the forbidden band zones is a cluster defect composed of two ormore defects adjacent to each other.
 7. The two-dimensional photoniccrystal optical multiplexer/demultiplexer according to claim 6, whereinat least one of the point-like defects each formed in each of theforbidden band zones is a cluster defect composed of three defectsadjacent to each other in the form of a triangle.
 8. The two-dimensionalphotonic crystal optical multiplexer/demultiplexer according to claim 6,wherein at least one of the point-like defects each formed in each ofthe forbidden band zones is a cluster defect composed of three defectsadjacent to each other on a straight line parallel to the waveguide. 9.The two-dimensional photonic crystal optical multiplexer/demultiplexeraccording to claim 8, wherein the cluster defect composed of threedefects adjacent to each other on a straight line is located on a fourthrow of the modified refractive index areas from the waveguide.
 10. Thetwo-dimensional photonic crystal optical multiplexer/demultiplexeraccording to claim 1, wherein the thickness of the modified refractiveindex area is 20 to 30% of the thickness of the body.
 11. Thetwo-dimensional photonic crystal optical multiplexer/demultiplexeraccording to claim 1, wherein the modified refractive index area is alow refractive index area whose refractive index is lower than that ofthe body.
 12. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer according to claim 11, wherein the lowrefractive index area is a hole.
 13. The two-dimensional photoniccrystal optical multiplexer/demultiplexer according to claim 5, whereinthe defect of the modified refractive index area is composed of amodified refractive index area whose thickness extends from one face ofthe body to 5 to 40% of a thickness of the body.
 14. The two-dimensionalphotonic crystal optical multiplexer/demultiplexer according to claim13, wherein the thickness of the modified refractive index area is 20 to30% of the thickness of the body.
 15. The two-dimensional photoniccrystal optical multiplexer/demultiplexer according to claim 5, whereinthe modified refractive index area is a low refractive index area whoserefractive index is lower than that of the body.
 16. The two-dimensionalphotonic crystal optical multiplexer/demultiplexer according to claim15, wherein the low refractive index area is a hole.
 17. Thetwo-dimensional photonic crystal optical multiplexer/demultiplexeraccording to claim 16, wherein the defect of the modified refractiveindex area is a donor type defect formed by not boring a hole in thebody.
 18. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer according to claim 16, wherein the defect ofthe modified refractive index area is an acceptor type defect formed byproviding a hole having a diameter larger than that of the other holes.